I will need to take metro line 2 to Shanghai People's Square and then line 1.

The operating hours of line 2 from PVG are 06:00 to 22:00. And the metro line 1 operates from 05:14 to 23:00.

Obviously, you cannot catch the subway when arriving at midnight. I suggest you take shuttle bus Night Line instead and it shall directly take you to People's Square. By the way, the bus operates from 23:00 (T1), 23:05 (T2) till 45min after the last flight arrives.